Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
| (i) | $\mathcal{G} \subseteq \mathcal{F}$ is a D470: Subsigma-algebra of $\mathcal{F}$ on $\Omega$ |
| (ii) | $E \in \mathcal{F}$ is an D1716: Event in $P$ |
| (iii) | $\sigma_{\text{pullback}} \langle I_E \rangle, \mathcal{G}$ is an D471: Independent collection of sigma-algebras in $P$ |
Then
\begin{equation}
\mathbb{P}(E \mid \mathcal{G})
\overset{a.s.}{=} \mathbb{P}(E)
\end{equation}